Latest on Poincare

A new 473-page paper by Gang Tian and my colleague John Morgan that gives a complete proof of the Poincare conjecture based upon the argument outlined by Grigori Perelman (which carries out the program of my other Columbia colleague Richard Hamilton) is now available as a preprint on the arXiv entitled Ricci Flow and the Poincare Conjecture. This paper is in the process of being refereed and should ultimately appear as a book in the monograph series that the Clay Math Institute publishes with the AMS.

Morgan and Tian just provide a proof of Poincare, not the full geometrization conjecture. Other sources for worked out details of Perelman’s argument are the notes by Kleiner and Lott, and the recent paper by Cao-Zhu that appeared in the Asian Journal of Mathematics. Cao-Zhu provide fewer details than Morgan-Tian, but do give a proof of geometrization. Until very recently the Cao-Zhu paper was only available in the paper version of the journal, for sale by International Press for $69.00. Yesterday the journal put the full paper on-line, and it’s available here.

Latest rumor I hear is that the Fields Medal committee has definitely chosen Perelman as a Fields medalist, with the appearance of these detailed proofs using his arguments clinching the deal. However it remains unclear whether he’ll show up in Madrid, or even actually accept the honor being offered him.

Update: There’s an article about this in this week’s Nature.

Update: The September issue of the Notices of the AMS has an excellent article by Allyn Jackson about this. Next week’s Science Times is supposed to have an article by Dennis Overbye.

Last Updated on

This entry was posted in Uncategorized. Bookmark the permalink.

106 Responses to Latest on Poincare

  1. Lilian says:

    By the way, how many fields medalists have been chosen this year? Tao, Perelman, who else would be a good candidate? I heard that there were going to be three of them?

  2. anonymouse says:

    Lindenstrauss, McQuillan

  3. Lilian says:

    Today’s New York Times (Science Times Section) convers news on Poincare Conjecture! Worth reading! 8-15-06 Tuesday

  4. comentator says:

    In the las ICM the “sure” bets (that were not) were:
    Tao, Borodin, so it is safe to say that in this time they could be amongst the winners and Perelman of course.

  5. Ghost of Marshall Hall says:

    Potential winners:

    As mentioned: Tao, Perelman

    Others (but likely some other time):
    Green, Pandharipande, Knutson, Darmon

  6. Jeremy says:

    After collecting information from the Hamilton’s paper (1982), Perelman’s three papers (2002, 2003), Cao-Zhu paper (2006), Kleiner-Lott paper (2006), Morgan-Tian paper (2006), as well as the articles by Sharon Begley (The Wall Street Journal), Allyn Jackson (AMS) and Dennis Overbye (The New York Times), a theory of the winners and losers in the proof of Poincare conjecture and the geometrization conjecture has been formed. The theory is described as follows:

    Theorem (Winners-Losers): There are winners and losers in the proof of Poincare conjecture and geometrization conjecture.

    The winners are: Hamilton, Perelman, Cao-Zhu, NSF, JSG Memorial Foundation, NSF of China, Harvard University and Tsinghua University in Beijing.

    The losers are: Kleiner-Lott, Morgan-Tian and Clay Mathematics Institute.

    The biggest loser: Clay Mathematics Institute. ||

    A complete proof of the Winners-Losers Theorem is given in the Appendix.

    Corollary: Losers speak first. Winners speak last. ||

    This corollary arrives naturally and it is even true in sports and politics.

    Appendix

    For later reference, we start by introducing the well-known Theorem of Publication.

    Theorem: Publish after the publication of others on solving the same problem equals publishes nothing, i.e.

    P(t) = 0 for t > t_(P of others).

    Here P stands for publication and t is time. ||

    Now we proceed to the details of the winner-loser theory.

    Hypothesis: All statements and claims made in the Cao-Zhu paper, Kleiner-Lott paper and Morgan-Tian paper are accurate and correct. ||

    The following is the proof of the Winners-Losers Theorem.

    Proof

    We first give proof of the winners.

    Hamilton had the vision to first introduce the equation of Ricci flow to the proof of the geometrization conjecture and laid the foundation for the Hamilton program. He has many mathematicians believed in and participated in the program. Perelman agreed that his own work was to carry out the Hamilton program. Cao-Zhu also acknowledged that their work is part of the Hamilton program. The final proof of the conjectures has vindicated Hamilton’s vision. Therefore, a winner. (Very likely, the Ricci flow equation will be renamed as the Hamilton Equation.)

    Perelman shared Hamilton’s vision and made the most critical contribution to push through the Hamilton program by bring in new ideas and new techniques, which made others realize that his claim to the proof of the geometrization conjecture, therefore the Poincare conjecture, could very well be true. Probably more importantly, the new techniques he developed will help the future development of mathematics. Although he left many less critical issues unsolved, some of those can be considered as details, the final proof of the conjectures has proved that his statement was accurate. Therefore, a winner. (The Poincare Conjecture will almost definitely be renamed as Perelman Theorem.)

    Cao-Zhu worked on the conjectures in secrecy, except to the Harvard mathematicians. They used much of the Perelman’s work, but did not limit themselves only on filling Perelman’s details, which enable them to keep a broader vision in pushing through the Hamilton program. After combining other people’s work with their new ideas, they could first publish a complete proof for the Poincare and geometrization conjuctures. Therefore, winners. (The geometrization conjecture may very well become Perelman-Cao-Zhu Theorem.)

    Cao-Zhu has certainly pulled off a coup when the publication of their paper was first announced in April 2006.

    NSF and JSG Memorial Foundation have been funding the work of Cao; NSF of China has been funding the work of Zhu. Obviously, funding winners makes them winners.

    Harvard University supported Zhu’s work; Tsinghua University in Beijing supported Cao’s work. Winner’s supporters are clearly winners.

    Now we give proof of the losers.

    Kleiner-Lott have been narrowly following Perelman’s work, but posted their findings for everyone to use. Unfortunately, they lost their concentration on the larger picture, the relationship of Perelman’s work with other people’s work. Filling in Perelman details has been proved not to be easy. The announcement of the forthcoming Cao-Zhu paper in April 2006 has been a surprise and total shock. Unable to complete their paper in time and were very much aware of the implication of the Theorem of Publication, Kleiner-Lott posted their unfinished paper on the non-refereed arXiv at the end of May, a few days before the appearance of the Cao-Zhu paper. Kleiner-Lott still plan to publish their paper, but after the publication of the Cao-Zhu paper and the Morgan-Tian paper, (Morgan-Tian paper uses many Kleiner-Lott’s results), the publication of their paper becomes much less meaningful considering the Theorem of Publication. Therefore, losers.

    Morgan-Tian have also been narrowly following Perelman’s work and busying on filling Perelman’s details. At the April 2006 announcement of Cao-Zhu paper’s publication, they haven’t even filled the details for a part of the Perelman’s work. Fully understood the implication of the Theorem of Publication, they sent a preliminary version (i.e. unfinished version) of their paper for refereeing in May, just before the Cao-Zhu paper’s June appearance, to show that their work was independent. The final version of their finished paper was posted on the non-refereed arXiv more than a month after the publication of the Cao-Zhu paper. By the implication of the Theorem of Publication, there will always be suspicion that the final version of the Morgan-Tian paper has been inspired and has benefited from the Cao-Zhu paper. Therefore, losers.

    The final version of the Morgan-Tian paper is more than 400 pages and only filled the details of a part of the Perelman’s work. Among other things, it certainly has proved that “the details for a genius could be major problems for common men”.

    As the supporter of the losers, Clay Mathematics Institute is obviously a loser.

    Finally, we give proof of the biggest loser.

    Clay Mathematics Institute has a big treasure chest to back up its list of millennium prize problems. However, whenever the millennium problems are concerned, Clay Institute should support the mathematics community as a whole (support its conferences, workshops etc.), rather than support individual mathematician(s). Its role should be of a referee rather than a player. Once it starts to support individual mathematician(s), it may be viewed as playing favoritism. Perelman might very well consider that Kleiner-Lott and Morgan-Tian are taking advantages of his work, under the support of Clay Institute. Other mathematician may think that Clay Institute intended to give the prize to mathematician(s) of their choice even before the problem is solved. The prize money may then be considered as “tainted”. The honor of the prize is therefore completely lost. The only thing that left is money. Giving out money that does not have widely recognized honor is truly meaningless. (There are people who really do not care about money!) Therefore, Clay Mathematics Institute is the biggest loser.

    End of proof.

  7. Student says:

    Does anyone know Hamilton’s opinion on the issue? Namely, Does he think that any of the “complete proofs” adds true substance to the solution?

  8. Lilian says:

    Hamilton gave a talk in the ICM, representing Perelman in receiving the prize. However, it seemed that he talked much about what he thought would work rather than describing what Perelman has done and the impact of his work. Probably he has taken ST. Yau’s flattering 50% contribution to the Poincare Conjecture and did not view Perelman’s contribution as important.

  9. woit says:

    Lillian and Student,

    I don’t believe Hamilton was “representing Perelman”, rather that he was invited to talk about his own work, and this invitation was issued long ago, when the IMU still hoped to get Perelman to come and speak himself. From hearing Hamilton talk about this, I see no evidence that he does not view Perelman’s contribution as important, quite the opposite. You’d have to ask him what he thinks of Cao-Zhu, I don’t know. But I’ve always had the impression that he hasn’t been all that interested in the project of filling in the details of Perelman’s proof using Perelman’s methods, preferring to see if he can use his own ideas to do some of the needed steps. He’s a very original mathematician, and such a person generally wants to do things their own way.

  10. werdna says:

    In their New Yorker article, the authors write:

    “Mathematicians familiar with Perelman’s proof disputed the idea that Zhu and Cao had contributed significant new approaches to the Poincaré. ”

    They then went on to quote only John Morgan to support this statement. It would have been more helpful to hear comments by other mathematicians, not just someone from the Morgan-Tian camp.

  11. Student says:

    I am not technically capable of evaluating the involved works, but am curious to know what the “consensus” is among experts.

    From what I read/felt, Morgan-Tian viewed their work as largely a community service — to help people understand Perelman’s proof (and Clay to legally claim Perelman a winner — to have a peer reviewed publication, albeit not by himself); they didn’t claim to have added anything substantial.

    Cao-Zhu however did claim substantial technical contributions, althoguh it is interesting that they said that they made them not because Perelman was wrong, but because they could not understand how he could, so they took on their own.

    The question is whether these “contributions” are substantial or not. Morgan thought they are not, but did not elaborate. and Yau seemed to think otherwise.

    When the PR storm about “crowning achievement” was going on in China, Hamilton was actually visitng that country (for “personal reasons”, as I heard — rumor has it that it involved a certain lady), and despite all the media fuss, he did not make any comment, other than that Cao and Zhu are excellent mathematicians. Being a close friend of Yau’s and the perceived authority on this matter, his silence could be explained as a withhold of endorsement (of course, it is totally possible he is just uninterested, especially given the non-math mess surrounding this).

    But then I read the abstract of Hamilton’s ICM talk and it mentioned Perelman AND Cao-Zhu.

    I agree that he probably wouldn’t feel that Cao-Zhu is a big deal even if it has substance (after all, these are details…). But I am interested in knowing how he put it into the context. Did he think that the deal was done 3 years ago (although we wern’t sure until now), or 2 months ago (with Cao-Zhu)?

    Lilian — if you were at his talk, could you shed some lights?

  12. Jessica Lau says:

    Read Silvia Nasare and Gruber’s elaborate portray of the Poincare Conjecture and Perelman. It’s an excellent piece of work! Accurate information! Fair report!!
    MANIFOLD DESTINY
    A legendary problem and the battle over who solved it.
    http://www.newyorker.com/fact/content/articles/060828fa_fact2
    What it says in the article is very accurate. But critics and supporters of Yau and others may be unhappy about what it says there. Well that’s the true story! I once read a review posted in this forum, reviewer was something like “Milnor the Giant” or something like that, that person is pretty fair and stood up to point out the unfairness and hierachy in mathematics community. It seems Yau is a fame seeker, well, different people may not feel the same way. But that guy’s review is just interesting.

    Perelman – Yau :The comparison very clearly establishes Perelman as a hero. He considered himself a disciple of Hamilton but only without Hamilton’s authorization–I think it’s a very modest yet somewhat souring comment that may has resulted from what Perelman felt about other people, in this case, Mr. Hamilton and Yau etc. As a Chinese myself, I deeply respect and admire Perelman yet feel a bit shameful of the other. Remember, not all Chinese mathematicians are like that. SS Chern, Loo-Keng Hua, Jingrun Chen, they are all humble and honest mathematicians.

  13. Herman says:

    Interesting report!! I think it’s very fair, honest and accurate report too! A few quotes from Perelam in Nasar and Gruber’s article:

    “It is not people who break ethical standards who are regarded as aliens,” he said. “It is people like me who are isolated.” We asked him whether he had read Cao and Zhu’s paper. “It is not clear to me what new contribution did they make,” he said. “Apparently, Zhu did not quite understand the argument and reworked it.” As for Yau, Perelman said, “I can’t say I’m outraged. Other people do worse. Of course, there are many mathematicians who are more or less honest. But almost all of them are conformists. They are more or less honest, but they tolerate those who are not honest.”

  14. Herman says:

    Yep! He’s right!! Expository article only deserves at most a Steele Prize!! It’s original ideas that open new field in research that’s of upmost importantce! I agree with you Jessica!

  15. Herman says:

    “Politics, power, and control have no legitimate role in our community, and they threaten the integrity of our field,” Phillip Griffiths said.

  16. Lilian says:

    Hi, Woit, I agree with most of your views, and that “(Hamilton) He’s a very original mathematician, and such a person generally wants to do things their own way.” But for the past ten years, he has not produced any significant results and his research hasn’t gone any further. Well, it would still be very interesting to see his own way of completing the program!

    Response to Student:
    Well, I believe Hamilton would be far more delighted in solving the problem himself rather than being a spectator of it for ten years. ST Yau once played a recorded speech that Hamilton commented on Chinese Mathematicians (in particular Cao, Zhu and Yau)’s contribution to Poincare conjecture (and Differential Geometry) and Hamilton did not emphasize the importance of Perelman’s contribution but Yau’s suggestive ideas. In his ICM talk, he even stated that he and Yau were the main developers of Ricci Flow. Well, I really don’t know how true that is. 1) What he said is true; 2) he just wanted to be nice to Yau or flatter him–you know, Yau is quite influential in today’s mathematics.

    Hamilton certainly made great contribution, but Perelman’s may be more of a revolutionary type. What you guys think?

  17. Lilian says:

    One forum http://www.popyard.com/cgi-mod/page.cgi?cate=1&page=1&r=0 that I came across attacked Silvia Nasar’s report! those are idiots. I am sure Nasar had received numerous harrassing emails from Yau’s supporters!!

  18. Matheu says:

    There is an article on a Chinese newspaper, Science Times, based on an interview with Shou-Wu Zhang, a Professor at Columbia University. It contains some interesting Q&A between Zhang and S-T Yau. The following is a translation:

    Zhang, “Can we call it Perelman-Zhu-Cao Theorem? ”

    Yau, “No. The contribution by Hamilton is the most, most important.”

    Zhang, “Should we call it Hamilton-Perelman Theorem?”

    Yau, “No. Strictly speaking, Perelman’s papers posted on the internet are just sketches of the proof. You can’t say that he proved Poincare and Geometrization conjectures.”

    Zhang, “Should we call it Thurston-Yau-Hamilton-Perelman-Zhu-Cao Theorem?”

    Yau, “That’s correct. Although the name is a bit long, it gives indication of everyone’s role.”

    [Note: I have edited this to fix it, the original version incorrectly dropped Perelman’s name from the last list of names.  PW]

  19. Student says:

    Folks, let’s focus on math. Last time I checked, Yau is an American.

    Again I am not working in this field, thus cannot judge if Silvia Nasar’s report is “accurate” on otherwise. I did read on the web that some in the field is very critical to the report (this is secondhand, since I don’t know the said commentator in person). This is complicated matter, so complicated that even experts within the field (in addition to those who have a stake) are still debating. I would not be surprised if Silvia Nasar’s report reflects the views of some, but not others, in the field.

    And precisely because of this complexity, I am very interested in the opinion of Hamilton’s own. Not that he has devine power to judge others, but after all, this is his theory, even though he got stuck on it until Perelman showed up.

    I feel a bit guilty that we have stretched the strig a bit too long on this one 🙂 But Peter has the advantage of being next to Hamilton (and Morgan), so maybe he can share with us something he overheard in the hallway 🙂

  20. Student says:

    This is from ICM Daily News:

    [Quote]

    Richard Hamilton (University of Columbia, New York, USA)
    finished his plenary lecture yesterday, the first of the
    ICM2006, by saying that he felt incredibly happy and enormously
    grateful to Grisha Perelman for finishing his work:“In
    this way we actually get a proof of the Poincaré Conjecture”

    … …

    Hamilton said that he had a “profound admiration” for
    Perelman’s work, and that he would be “delighted to
    work with him in the future”. He said that he had met
    Perelman personally, but he was not prepared to comment
    on Perelman’s refusal to accept the Fields Medal
    conferred on him on Tuesday at the ICM2006. However,
    Hamilton did say that “it is not fair to criticize his
    position”.

    Hamilton was also asked abut the Chinese
    mathematicians Xi-Ping Zhu, from the University of
    Zhongshan (Canton, China), and Huai-Dong Cao, from
    the Lehigh University in Pennsylvania (USA), who last
    June published a paper in the Asian Journal of
    Mathematics. In the abstract of this paper the authors
    state that they present “a complete proof of the Poincaré
    and Geometrization Conjectures”. Hamilton is sure that
    “there is no controversy” because both mathematicians
    are “great researchers”. According to Hamilton, the
    controversy surrounding the proof of Poincaré’s
    Conjecture was caused by the press. He went on to say
    that Perelman’s work “is difficult to understand” and at
    some points even Perelman himself employs the term
    “sketch”. “A sketch is an invitation to complete a finished
    work, to find a way of doing it better. But no criticism is
    implied in this, only the wish to help to solve a problem.
    There is no controversy involved. Grisha is a model of
    decorum and there is no dispute about who did what”.

    … …

    [/Quote]

    Very diplomatic. Still no answer to my question, but I guess that’s all we could get out of him …

  21. tg says:

    Dear Lilian, Jessica Lau et al,

    Re: Nassar and Gruber’s report.

    I agree that the article in question is very entertaining and probably an accurate reflection of the events. However, I also believe that it exploits stereotypes against the Chinese as “technicians” and uncouth (the latter is my own word). It singles out Yau, connects him deeply with Chinese mathematics, while downplaying the fact that many mathematicians (and academics) act very similarly although in much less famous circumstances.

    I and my colleagues on the “2006 Fields medal winners” forum of this blog have debated the relative merits of these points at length, so I kindly point you to the discussion there.

    My purpose in introducing this link of discussion is to counter Lilian’s assertion that “attackers” of Nasar and Gruber’s report are “Yau supporters”. In my case, I support myself — I am of Chinese (descent) — as are you, Jessica Lau. Don’t you think that stereotyped attacks against a figurehead such as Yau (“figure head” — a position that Nasar and Gruber go at length to assert, although it is irrelevant mathematics involved) affect Chinese (and asian) opportunities in academics? I do.

    I also kindly point you to September’s Notices of the AMS article (available online at http://www.ams.org/notices/200608/200608-toc.html)
    where further discussion of the position of Asians in mathematics is discussed.

  22. Peter Woit says:

    student,

    I’m not at all informed about Hamilton’s current views, know Morgan’s much better, but in neither case would it be appropriate for me to repeat things here they told me privately. I can say that everything I’ve heard from them is consistent with what they are saying publicly. Morgan worked hard for a long time on the project with Tian of writing up a complete proof of Poincare, and in the end found that Perelman’s sketch of a proof held up, you really can fill in all the details. As he told Nasar, he sees the Cao-Zhu version as also closely following the Perelman sketch.

    As for Hamilton, ever since Perelman’s papers came out, lots of people have wanted to know if he thinks Perelman’s sketch can be completed to a true proof. My impression is that this is just a question he’s not very interested in, that he’s also not interested in getting involved in the politics of this, and he hasn’t wanted to talk to the press. He agrees that Perelman has come up with important new ideas, and I think what he is interested in is seeing what he can do by putting these together with his own techniques.

    One interesting thing about the Nasar article was Perelman’s comment about how grateful he was to Hamilton for Hamilton’s openness, generosity, and willingness to share his ideas. Since he has been here at Columbia, Hamilton has often run a seminar, in which he discusses in detail his latest work in this area and shares with others what he has been figuring out. His contributions to research in this area go beyond what is just in his published papers.

  23. Student says:

    Thanks Peter. I particularly appreciate the comment about Hamilton.

  24. Matheu says:

    Peter, thanks. Could you please re-edit to remove my correction?

    Now, from Morgan’s public talk, he says the following about the credit for proving Poincare conjecture, contradicting to what Yau said.

    “Can we say that Perelman has proven the Poincaré Conjecture?
    Yes, I would say and I will say today that Perelman has proven the Poincaré Conjecture. But one has to understand that he would not have done it without Hamilton’s work. Yet, in the culture of mathematics it is my view that the credit for proving the Poincaré
    Conjecture should go to Perelman.”

  25. TruthSeeker says:

    From reading the NewYorker article, I did not get any impression about stereotypes that tg mentioned above, and neither did many others who posted here and elsewhere in the blog. Instead, I had the feeling that the authors were trying to write a hero-villain story with Yau being the bad guy and Perelman the hero, of course. His heritage was mentioned in order to give context to and help explain his behavior. (There is the quote, e.g., “Yau’s not jealous of Tian’s mathematics, but he’s jealous of his power back in China.”) So I thought it was necessary that the authors describe his Chinese roots.

    However, I thought they were too eager to portray him as the villain that they failed to mention relavant, important details about his life. For example, it is well known that Yau has been passionate about fighting corruptive practices in academia in Communist China, to the point of being censored by the PRC. He is also known to be the rare scholar who insists on not taking a salary when lecturing or engaging in other scholarly activities in China, even though generous compensations must have been offered him, being who he is.

    But such stories were not told in the article, because they would weaken their thesis that Yau was dishonest or manipulative. Whether he is dishonest or not in the handling of this Poincare incident, I do not know. It may very well be that he honestly thinks Perelman’s proof is too sketchy and that filling in those details is far from routine or straightforward. Let the mathematical community take the time to go through all the manuscripts carefully, and let them give their most objective opinion, without the influence of politics. If it is determined that Yau is wrong (in his assessment), then I think he should apologize one way or another. We must give credit where credit is due.

  26. tg says:

    Dear Truthseeker,

    You raise an important question with respect to the ways in which mathematicians (academics) assign credit, which I think deserves communal analysis, since it’s often subjective. Here are a few (common) scenarios.

    (1) “A” claims a solution to a problem, gives the statement of the solution (e.g., a formula) that is clearly brilliant and nonobvious, and by all checks (e.g., by computer) is correct, and says the proof is by induction, but leaves all the details out. “B”, needing the formula finds no proof (and “A” will not respond to his questions about the proof) and goes about doing the induction. It’s hard work, but eventually an induction proof works. Afterwards “A” says “I told you so”. But where was he when the details were being worked out?

    (2) Same as (1), except “A” doesn’t claim to have a proof, but says _probably_ an induction works.

    (3) “A” says he knows how to solve a problem but isn’t there yet, and tells people his progress. “B” hears about “A”‘s work and with hard work completes the proof.

    (4) Same as (3) except “A” says he’s done what he can do.

    (5) The same as (1)-(4), except “A” and “B” are actually friends. They wonder whether it’s appropriate to coauthor a paper together.

    In all scenarios “A” clearly deserves credit, in my opinion. But what about “B”?

    Personally, I think “A” is a jerk in scenario (1), but realizes that if he allows scenario (2) then he’ll be a sucker, since mathematicians usually credit the person(s) who finish the job, and he wants all the credit to himself. As humans, we don’t like people dishonestly exploiting other’s hard work for their own fame — in which case maybe we should highly credit “B”‘s work, since we wouldn’t want to fall into, gasp, physics like rigor.

    In (3), “B” is a usually regarded as a “thief”, but in (4) he’ll be given excellent credit as the “finisher”.

    In (5), they could fairly write a paper together, and the result would be the “A-B’s theorem” for all time.

    How do Perelman, Hamilton and Yau et al. fit into these scenarios?
    No one doubts Perelman’s contribution! But whether Yau et al deserve any credit depends (in the above scenarios) highly on what Perelman claimed know or not know.

    One could argue that clearly it wasn’t so obvious to even Perelman that he actually solved Poincare, or he would have dared to say so in his papers, right?

  27. Deane says:

    “One could argue that clearly it wasn’t so obvious to even Perelman that he actually solved Poincare, or he would have dared to say so in his papers, right?”

    In fact, in his third preprint, Perelman quite explicitly claims to prove the Poincare conjecture. He just doesn’t call it the “Poincare conjecture”. If I recall correctly, he calls it the “elliptization conjecture” (parallel to Thurston’s “hyperbolization theorem”), but its statement is exactly that of the Poincare conjecture.

  28. tg says:

    Dear Deane,

    I stand corrected then!

  29. TruthSeeker says:

    tg,

    Questions about assigning credit and authorship can in some cases be tricky indeed. Even guidelines such as those issued by the AMS (see http://www.ams.org/secretary/ethics.html) are only that — guidelines. For example, their website says that researchers have the responsibility to publish “full details” of their (new) results. But the word “full” is not well defined. Did Perelman’s papers, for example, contain full details? I think different experts will have different opinions on this matter. I guess that’s why a committee called COPE (Committee on Professional Ethics) was set up by the AMS, an important function of which is to handle disputes. But even their final decision is only an opinion, a “best” judgment arrived at by examining the circumstances of the individual case and the existing practices and conventions of the field. And different fields do have different standards. (In chemistry, e.g., it is typical to automatically add an advisor’s name to a graduate student’s paper, regardless of contributions made, but this practice is much rarer in mathematics.)

    Regarding the various scenarios you listed, let me offer my best opinion. In cases 1, 2, and 4, “A” cannot expect to publish his result by itself in a mathematical journal without a proof, even though his formula may be correct. If “B” comes up with a proof, I think he is obligated to list “A” as a co-author, assuming that the formula has not been published elsewhere before.

    In the case of (3), B’s behavior could lead to a poor reputation at best or plagiarism at worst (if he doesn’t give proper credit in his paper containing the ideas of “A”). Ideally, he should have discussed his intention with “A” and work out some kind of a joint authorship.

    You may want to look at other examples discussed in the COPE manual (http://www.ams.org/secretary/copemanual.pdf).

  30. Whu says:

    When reading this thread, I think one question has not been answered. Who should we blame for Dr. Perelman’s feeling of be isolated?

    In that article in “New Yorker” by Nasar, the author tried to convince audience that Dr. Perelman wanted to be isolated because of the dishonest or dictatorship of YAU. Is it true?

    Dr. Perelman, who at least provided a schetch to prove Poincare conjecture, left the US in 2003 and stayed away from the math world since then. Yau and his students started their journey in 2004 funded by NSF, to investigate Dr. Perelman’s proof. They completed it in May 2006. Assume YAU has attempted to take credits from Dr. Perelman. But this must have happened very recently in 2006. However, Dr. Perelman have the feeling of being isolated because of dishonest back in 2003 and beyond.

    I, a teacher of chinese national, doubt the author’s intention. I admire Dr. Perelman’s terrific work and that of Yau too, about which I actually can only understand the first page of their papers. However, I feel uncomfortable that the author distorted the fact and made Yau a Godfather from Chinatown, which, seems to me, one of the strerotypes some in the US and Europe feel comfortable when thinking about China or anybody related to China.

  31. TruthSeeker says:

    I don’t think Perelman attributed his sense of isolation to Yau, or at least not solely or primarily to him. It says in the article that “he
    mentioned a dispute that he had had years earlier with a collaborator over how to credit the author of a particular proof, and said that he was dismayed by the discipline’s lax ethics.” And, regarding Yau, he said: “I can’t say I’m outraged. Other people do worse…” He seems to be saying that there are worse offenders in the math community.

  32. MathLover says:

    Peter,

    Thanks for your blog and discussions here. I’m a math lover and of origin from China. The discussion about Poincare conjecture and Perelman has now a new dimension. Let me first quote two posts below:

    Jessica Lau Says:
    August 25th, 2006 at 3:18 am
    http://www.math.columbia.edu/~woit/wordpress/?p=434#comment-15043

    “Perelman – Yau :The comparison very clearly establishes Perelman as a hero. He considered himself a disciple of Hamilton but only without Hamilton’s authorization–I think it’s a very modest yet somewhat souring comment that may has resulted from what Perelman felt about other people, in this case, Mr. Hamilton and Yau etc. As a Chinese myself, I deeply respect and admire Perelman yet feel a bit shameful of the other.”

    TruthSeeker Says:
    August 26th, 2006 at 2:10 am
    http://www.math.columbia.edu/~woit/wordpress/?p=434#comment-15091

    “I had the feeling that the authors were trying to write a hero-villain story with Yau being the bad guy and Perelman the hero.

    However, I thought they were too eager to portray him as the villain that they failed to mention relavant, important details about his life. For example, it is well known that Yau has been passionate about fighting corruptive practices in academia in Communist China, to the point of being censored by the PRC.

    Let the mathematical community take the time to go through all the manuscripts carefully, and let them give their most objective opinion, without the influence of politics.”

    I’m very thankful for TruthSeeker’s remark about Yau’s fighting against the corruption which has an intrinsic link to his own student Tian Gang. There is a big fight of corruption in China. Unfortunately, the corruption has swept out to academic and education areas as well. Goverment has shown only little effective control of the situation. Some (not all) scholars are corrupt; more severely, the system is corrupt. Tian is a part of this system. They promote and cover each other. It’s a shame to hide this from the international community. Jessica, why not shame on yourself, you seem to enjoy the distorted report about Yau. I admire Perelman and Yau both.

    I want to remind a story. Last year, an audit of an american firm (listed in NY) has lead to arrest of a high ranking corrupt officer in Chinese version of FDA. It seems that we shall push a similar pressure from outside to uncover the corrupt Chinese oversea scholars like Tian. There are several of them. Their images have damaged the fame of all other Chinese scholars. I can image, a tax audit will show they may hide their very high incomes from China.

    Does Sylvia Nasser has interest to uncover it? Or shall we leave it to Dennis Overbye? It is not entertainment, it’s more serious. Much more.

  33. Matheu says:

    Morgan just declared that Perelman proved Poincare Conjecture in
    2003. See the August 26 Daily News of ICM2006.

    If we believe what Professor Morgan said, then what Yau did — he announced to the Chinese media that Chinese mathematicians gave the first complete proof of Poincare conjecture— is very bad. He should have known that such an announcement would cause controversy. Even worse, he accepted the paper by Cao-Zhu without stringent refereeing process and forbid the editors to read it.

  34. Who says:

    http://www.icm2006.org/dailynews/

    click on August 26
    article reporting Morgan’s talk starts on page 2

    http://www.icm2006.org/dailynews/dailynews26.pdf

  35. geometer says:

    “When reading this thread, I think one question has not been answered. Who should we blame for Dr. Perelman’s feeling of be isolated?”

    I do not think there is anyone here to blame (certainly not Yau; in fact, I doubt Perelman cares what Yau thinks of does).

    “In that article in “New Yorker” by Nasar, the author tried to convince audience that Dr. Perelman wanted to be isolated because of the dishonest or dictatorship of YAU. Is it true?”

    I do not see anything in the article that suggest the above. According to Nasar, Perelman explicitly say that “other people do worse”, so this is not about Yau. I think, Perelman’s reason is that, now that he is famous, he can no longer keep silent about what he thinks is wrong in math, while speaking up is not in his nature, so he has to quit.

  36. tg says:

    Dear geometer,

    I can’t be sure who Perelman blames for him leaving math. I don’t think his “others do worse” remark exculpates Yau in his mind (or mine). Surely he (or perhaps Nasar and Gruber in their arguably highly biased article, written to appease the popular anti China sentiment in today’s media) wants to come out saintly and would rather not explicitly say Yau is the cause of all (or much of) his problems.

    It’s worthwhile to emphasize that in the article reference is made to how Hamilton showed up late to a Perelman’s lecture, or seemed indifferent. Perhaps Hamilton is also to blame in Perelman’s mind (I speculate only based on the article, I don’t know much about their dealings). Note, however, that this is internally consistent with Perelman’s assertion that he is a disciple of Hamilton — what worse than to have that one special person who you think will fully appreciate your efforts seem less than caring?

    His behaviour is consistent with an academic who feels under-appreciated and scorned. Of course, this is difficult for most of us to imagine — given the nice (for mortals) opportunities he was given in terms of academic positions in the US, well before his recent work. But maybe he expected even more. The standard conclusion now is that he proved that he did.

    BUT, I want to write about another point of view on the unfortunate impact of Perelman’s decisions to date. This is separate from the discussion of the controversial attitudes of Yau et al, which has received ample treatment in other comments.

    Media, and future mathematicians are going to look at the model of Perelman for years to come. Do we really want the conclusion to be that mathematics is about the “lonely genius” who is incommunicative, terse, and eventually gave up on the pathetic subject that was thankless?

    Frankly, if this is his attitude, I’d rather that he keep on doing (or not doing) his work from elsewhere — I’d rather not have him as part of any department I’m in (that being said, departments hoping to have him wouldn’t be too interested in me!). I know various prestigious institutions would disagree — but I’d rather have faculty that are lecturing, developing graduate students, publishing, and in general contributing to the health of mathematics around me. I can always read his papers online.

    The last thing the subject needs is for the public to think is that the Perelman model is what should be strived for. We have to constantly explain pure mathematics’ virtue to the public, and to our peers, and to our financial sponsors. If we celebrate how to achieve this with a society of loners who hole up for a while and eventually (or probably not) create something, then I think mathematics is in trouble.

    Imagine the following NY times article:

    “XYZ a million year old problem got solved by this angry loner who hates everyone around him, and finally got his chance by ignoring and quitting math after proving he could solve what they couldn’t. XYZ is this important math problem which is about donuts not looking like oranges. Mathematicians say that this could be relevant to black holes, but secretly many say that’s just happy talk for the benefit of this article. Truthfully, an average engineering group at an average engineering department produces more relevant science for the work in a given year than XYZ will do for all of time. Finally, this problem would likely have been solved much earlier if there was more communication involved, but that’s math.

    Some-one-isomorphic-to-Sylvia Nasar-reporting”

  37. tg says:

    I think the “other people do worse” line is overplayed and can hardly exculpate Yau (in Perelman’s mind). It can easily be interpreted as a public relations statement.

    On the other hand, notice the article also points to the possibility that _Hamilton_ contributed to Perelman’s disappointment. Specifically I speak of the passage concerning Hamilton’s lack of keenness in Perelman’s work.

    In general, I don’t agree with the model of mathematical research that the Perelman case exhibits. As a community, I think mathematics would be better off supporting and exhaulting collaborative, communicative academics than the “lonely genius” who rejects the field.

    The fact that this lonely genius did manage to solve an old problem whose solution is only understood by a handful of people isn’t an end that supports the means, in my opinion. Don’t buy that nonsense about Poincare being relevant to black holes, or whatever. Any average engineering dept group probably produces more for this world and science in general than Poincare likely ever will. That’s the bottom line when it comes to asking for public funding for our field.

    If Perelman doesn’t want to continue in mathematics, that’s sad. But academic life is tough, and asks for many contributions beyond solving hard problems. He’s been given plenty of opportunity and laudation at this point. I don’t think it serves either mathematics or Perelman to massage him (or those who might sympathize with him) any further.

  38. Phil says:

    woit writes

    “It’s certainly true that after someone has come up with a new idea, it often looks “obvious” and it’s hard to understand why it was so difficult to find it. But, in this case you can look at what people had to say before the ideas were there….”

    Perfectly stated. That is key point.

  39. Moeen says:

    Given that there seems to be quite a debate over the quality of the recent article “Manifold Destiny,” I thought it might be worth putting up my own points on it, so here goes:

    Concerning the authors’ supposed bias against the Chinese, I have to say when I first read the article I certainly didn’t feel there was any bias of the sort in there, and was somewhat surprised to find commentators here claiming that. Looking at their comments, it seems like they’re just read some parts of the article the wrong way and over-reacted.

    For example, the accusation that the article stereotypes Chinese mathematicians as having strong technical skills is probably due to the quote by Griffiths referring to Yau where he says “He was not so much thinking up some original way of looking at a subject but solving extremely hard technical problems that at the time only he could solve, by sheer intellect and force of will.” This isn’t stereotyping, just pointing out what Yau’s style of doing mathematics is. For example, the authors point out that Perelman’s style is similar, and even compare him to Yau saying “Like Yau, Perelman was a formidable problem solver. Instead of spending years constructing an intricate theoretical framework, or defining new areas of research, he focussed on obtaining particular results.”

    Also, the authors aren’t attacking the Chinese mathematcs community in pointing out Yau’s status there. Their goal in this case is to show that Yau more or less wants to be the head of the mathematics community in China. Although Yau is an american, he seems to want to be seen as a hero for China. The authors state that “Yau believed that if he could help solve the Poincaré it would be a victory not just for him but also for China.” and moreover:

    Though Yau had not spent more than a few months at a time on mainland China since he was an infant, he was convinced that his status as the only Chinese Fields Medal winner should make him Chern’s successor. In a speech he gave at Zhejiang University, in Hangzhou, during the summer of 2004, Yau reminded his listeners of his Chinese roots. “When I stepped out from the airplane, I touched the soil of Beijing and felt great joy to be in my mother country,” he said. “I am proud to say that when I was awarded the Fields Medal in mathematics, I held no passport of any country and should certainly be considered Chinese.”

    Although Perelman does seem to fit the stereotype of the ‘lonely genius,’ the article seems to imply that was not his intention: In 1996, he wrote Hamilton a long letter outlining his notion, in the hope of collaborating. “He did not answer,” Perelman said. “So I decided to work alone.” The authors also point out that “Mathematics, more than many other fields, depends on collaboration,” so they aren’t supporting the ‘lonely genius’ model.

    I’ve discussed the article with a few mathematicians, and they’ve said that the article was a bit ‘gossipy,’ but was factually accurate. Yau’s negative behavior seems to be common knowledge in the mathematics community, and all the article did was make it public. None of them had anything negative to say about Tian.

    It seems like Perelman left the community because he didn’t want to get involved in the politics of it, which he saw as unethical, and this would no longer be possible given his current fame. It seems that given Perelman’s reasons for leaving, the writers of the article probably wanted to give an example of this sort of unethical behavior, and Yau was the obvious choice. While Perelman’s abandonment is somewhat unfortunate, I hope the mathematics community takes note and does something about this sort of behavior. I for one would not want to waste time having to deal with baseless accusations, character assassinations, and arguments over priority. This sort of thing is detrimental to research and the community.

    Overall, a good article, which, despite being somewhat ‘gossipy,’ was well written.

  40. Whu says:

    Moeen Says:

    “Concerning the authors’ supposed bias against the Chinese, I have to say when I first read the article I certainly didn’t feel there was any bias of the sort in there, and was somewhat surprised to find commentators here claiming that. Looking at their comments, it seems like they’re just read some parts of the article the wrong way and over-reacted.”

    I trust you are honest when saying these. However, I would like to propose a conjecture here. Let us call it Nasar’s Conjecture.

    Nasar’s Conjecture: Bias or stereotype of a doughnut size can be rendered into the size of a point in people’s mind when it has been applied CNN flow.

    Discussion of Nasar’s Conjecture:

    I and some of my friends found a trick American media always use when reporting other countries, especially China. Whenever the word “China” could not be avoided, it must be appeared in the report with phrases like “Communists, Human rights, claiming Taiwan and Tibet”. For a country in Africa which US dislikes, the used phrase would be “corrupted, AIDS, civil wars, etc”. This trick has been used in the extreme by CNN. Hence, we name it CNN flow.

    Using this CNN flow, people without any knowledge about China or countries in Africa will naturally think “This is it over there”, and hence bias no more when the word “China” is bound to “communist, human rights, abortion, take off human organ, invade Taiwan/ Tibet/Mongolia”. However for people from China, the feeling is totally different.

    I am sorry to introduce politics to this elegant and decent forum and I will not be upset if the editor decides to remove it. My point is: bias or not is up to each individual.

    A sketch of a proof for Nasar’s Conjecture:

    Nasar’s article portrays a bad guy, called YAU, who is dishonest, behaves like communist china, seeks fame and power crazily, promotes communist china insanely. In one word, really bad! While Dr. Perelman, a man from a remote planet, is the beloved and cutest kids we ever have.

    A complete proof of Nasar’s Conjecture:

    Waiting for volunteers to fill in the gaps!

  41. Moeen says:

    Whu Says:

    “A sketch of a proof for Nasar’s Conjecture:

    Nasar’s article portrays a bad guy, called YAU, who is dishonest, behaves like communist china, seeks fame and power crazily, promotes communist china insanely. In one word, really bad! While Dr. Perelman, a man from a remote planet, is the beloved and cutest kids we ever have.”

    But the problem is you assume that the characterization of Yau’s behavior, and Yau himself, is representing China in the article, whereas the authors are not doing this this but showing that Yau wants to be seen as the leader of mathematics in China. His behavior, while shown in contrast to Perelman, is specific to Yau, and should be seen in context of the Yau-Tian rivalry.

    For instance, the authors make a point that Yau’s behavior is characteristic of “the squabbles over priority which disfigure scientific history,” which the authors quote from E. T. Bell’s “Men of Mathematics.” The authors give an example of this kind of squabble involving Poincare and Klein, and say:

    “An exchange of polite letters between Leipzig and Caen ensued. Poincaré’s last word on the subject was a quote from Goethe’s ‘Faust’: ‘Name ist Schall und Rauch.’ Loosely translated, that corresponds to Shakespeare’s ‘What’s in a name?’

    This, essentially, is what Yau’s friends are asking themselves.”

    The authors are not at fault if you insist on seeing things as if they’re being portrayed from an american stereotype of Chinese behavior, and this discussion will also go nowhere.

  42. not a mathematician says:

    Perelman succeeded in proofing one more thing: when the goal is close, awarding prizes pushes scientists to exhibit their worst side. The Clay institute will have to choose if they support mathematics or speed races.

  43. tg says:

    Dear Moeen,

    I was one of the people who felt Nasar and Gruber’s article was “biased” (i.e., motivated to sell magazines to the vast anti-China sentiment reading the Newyorker, at the expense of asian mathematicians and mathematics more generally). I can tell you that I read their article quite carefully.

    Obviously, all they said may very well be true, while still leaving a biased/stereotyping article, if they decide to leave out other facts or context. All I claim is that that is what they do, AND they had the motivation to do it. I’ve written more than enough here and elsewhere on this blog to describe how I think they do this.
    I’d prefer, as a point of pedagogy to construct a non-China example to illustrate this point, but you can try your own, if you like, as an exercise.

    The danger of racism/nationalism/sexism is its subtlety. Sometimes its hard to notice a particular brand unless you’re dealing with it yourself. Part of the problem is many asians do not even recognize it affecting them, since they are told that they are already “overrepresented” as a minority in academics, so how could there be a problem? Perhaps with further discussion, such as the article written in September’s Notices of the AMS, this will change.

  44. TruthSeeker says:

    An article may be well-written, factually correct, and still be an incomplete or one-sided representation of truth/reality. Surely a talented writer can skillfully select only a portion of facts available to him/her to weave a good story to achieve a certain effect.

    Unfortunately, that’s also how some scientists do “science.”

  45. any says:

    〉Dear Ms Nasar:

    > First let me say that I have been a subscriber to The New Yorker
    > since the 1960’s; I love the magazine, and read nearly all the
    > articles every week.
    >
    >I am also a co-author of Yau’s,?and since 1991, and we have
    > written 18 joint papers.?Of course, not all of them are major
    > breakthroughs, but at least 2 of them can be so designated: our 2000
    > paper which appeared in Nuclear Physics B, and our 2006 paper which
    > just appeared in the prestigious journal “Communications in
    > Mathematical Physics”.?It is extremely rare for mathematicians to get
    > a paper published in a journal devoted to nuclear physics, and our
    > 2006 paper solves a problem dealing with stability of Black-Holes,
    > first elucidated by the Princeton physicist John Wheeler in 1957.?
    > These papers ALONE demolish your statement that Yau has had no major
    > results in the last 10 years.?How could you have made such a
    > statement??Where did you get your inxxxxation? Didn’t you feel a
    > responsibility to check your facts with other mathematicians??Your
    > behavior reminds me of the Jason Blair scandal at the New York Times.?
    > Shame on You!
    > Sincerely yours,
    > Joel?
    >
    >
    >
    >
    > Best regards,
    > Joel

  46. Moeen says:

    TruthSeeker Says:

    “An article may be well-written, factually correct, and still be an incomplete or one-sided representation of truth/reality. Surely a talented writer can skillfully select only a portion of facts available to him/her to weave a good story to achieve a certain effect.

    Unfortunately, that’s also how some scientists do ‘science.’ ”

    That’s certainly true, and the article was a bit ‘gossipy,’ if you will. My main point, however, is that the authors were not racist or stereotyping. The characterization of Yau’s somewhat egotistical behavior is specific to him alone; for example, none of the other Chinese mathematicians mentioned in the article are described that way.

    If anyone believes otherwise you’ll have to be more specific, or the discussion just degenerates into making accusations.

  47. atomistic machiavelli says:

    “Moeen Says:
    This isn’t stereotyping, just pointing out what Yau’s style of doing mathematics is. For example, the authors point out that Perelman’s style is similar, and even compare him to Yau saying “Like Yau, Perelman was a formidable problem solver. Instead of spending years constructing an intricate theoretical framework, or defining new areas of research, he focussed on obtaining particular results.”
    .

    The authors are not at fault if you insist on seeing things as if they’re being portrayed from an american stereotype of Chinese behavior, and this discussion will also go nowhere.”

    When dealing with the dregs of defensive nationalism, with the opium smoke still hanging in the air, you find that parsing every phrase to quark dimensions is never sufficient.

    Always expect that even smaller particles will be hypothesized and synthesized as necessary for the next round, until untestability is
    securely in hand.

  48. ty says:

    How could SYLVIA NASAR AND DAVID GRUBER turn in their expense reports to their boss at the New Yorker magazine and to justify their travel expenses IF they failed to catch Perelman in person in his “dimly lit hallway of the apartment” and came home empty-handed?

    How could SYLVIA NASAR AND DAVID GRUBER justify their travel expenses to their boss at the New Yorker magazine IF they failed to come up with some spicy stories and gossip materials to stir up the pot?

  49. Mike says:

    Anderson was quoted in the (New Yorker) article:
    “Yau wants to be the king of geometry,” Michael Anderson, a geometer at Stony Brook, said. “He believes that everything should issue from him, that he should have oversight. He doesn’t like people encroaching on his territory.”

    Michael Anderson responded to The New Yorker magazine:

    “The New Yorker article badly distorted my comments and
    the quote given is very inaccurate and misleading. I’ve already
    discussed it with Yau and expressed to him my apologies and disgust
    at using my name in this respect. I tried to have the quote removed,
    but was unsuccessful, partly because I was travelling in Europe while
    all this happened very quickly and I had no time respond.
    I spent a good deal of time talking with Sylvia Nasar
    trying to convince her to avoid discussion of the Tian-Yau fight
    since it is irrelevant to Perelman, Poincare, etc. But obviously I
    was not successful. In this particular respect, I feel the New Yorker
    has done a disservice to mathematicians.

    Sincerely, Michael Anderson”

Comments are closed.